GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Aug 2018, 15:46

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Maths, Physics and chemistry books are stored on a library

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Director
Director
avatar
Joined: 10 Feb 2006
Posts: 647
Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post Updated on: 02 Apr 2014, 22:09
2
12
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

73% (03:00) correct 27% (02:37) wrong based on 365 sessions

HideShow timer Statistics

Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book?

A. 1/10
B. 3/20
C. 1/5
D. 1/4
E. 9/20

We know that M = 2P
P = 4 + C
M = 8+2C

8 + 2c + 4 + c + c = 20
4c + 12 = 20
4c = 8
c = 2 , P = 6, M = 12

Please assist further. Thanks

_________________

GMAT the final frontie!!!.


Originally posted by alimad on 26 May 2008, 12:01.
Last edited by VeritasKarishma on 02 Apr 2014, 22:09, edited 3 times in total.
Edited the question
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8199
Location: Pune, India
Re: Combination  [#permalink]

Show Tags

New post 30 Mar 2014, 19:44
5
2
Mackieman wrote:
Please help me with this one.

Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?

Chemistry books: 2
Physics books: 6
Math books: 12

Sum = 20

P(Chemistry) = 2/20 = 1/10
P(Hard cover) = 8/20 = 4/10 = 2/5

P(AuB) = P(A)+P(B)-P(AnB)

P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50

P(AuB) = 5/50 + 20/50 - 2/50 = 23/50

P(AuB) - P(AnB) = 21/50 (since either means that we don't want both)

What is wrong here? (OA: 9/20)


Everything is correct except this: P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50
P(AnB) is given by the product of individual probabilities when the events are independent.
How many Chemistry books are hardcover? There are total 8 hardcovers and 7 belong to Math and Physics. This means there is only 1 Chemistry hardcover book out of total 20 books.
So P(AnB) = 1/20

Now P(AuB) = 1/10 + 2/5 - 1/20 = 9/20
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Most Helpful Community Reply
Intern
Intern
avatar
Joined: 26 Oct 2013
Posts: 22
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 30 Mar 2014, 10:32
5
2
First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:

m + p + c = 20 (since 4/5 of the 25 spots are full of books)

m = 2p

p = 4 + c

From that, you can use Substitution to get everything down to one variable.

c = p - 4

m = 2p

p = p

Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.

With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways to "win" - either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, 9 provide the desired outcome, making the answer E.

Note - a common trap answer here is A, as people forget that "2 chem + 8 hard" double counts the one book that is "both". Venn Diagram logic can be helpful to avoid that trap, or in cases like this with relatively small numbers it may be even more convenient to just write out the possibilities.
General Discussion
Director
Director
avatar
Joined: 23 Sep 2007
Posts: 760
Re: Combination  [#permalink]

Show Tags

New post 26 May 2008, 12:24
alimad wrote:
Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 4 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?

1/10
3/20
1/5
1/4
9/20


the shelf has the capacity of 25 books, 20% empty (5 books), the shelf has 20 books

Phys = 1x
Math = 2x
chem = x - 4

1x + 2x + (x - 4) = 20
4x - 4 = 20
4x = 24
x = 6
x - 4 = 2

So the shelf only has 12 math, 6 phys, 2 chem books

If there are 12 soft covers and 8 hard covers, and 4 hard covers are math/phys, then 4 hard cover must be chemistry, BUT there are only 2 chemistry books.
Manager
Manager
avatar
Joined: 20 Dec 2010
Posts: 163
Location: Stockholm, Sweden
Re: Combination  [#permalink]

Show Tags

New post 02 Jan 2011, 12:19
1
Please help me with this one.

Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?

Chemistry books: 2
Physics books: 6
Math books: 12

Sum = 20

P(Chemistry) = 2/20 = 1/10
P(Hard cover) = 8/20 = 4/10 = 2/5

P(AuB) = P(A)+P(B)-P(AnB)

P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50

P(AuB) = 5/50 + 20/50 - 2/50 = 23/50

P(AuB) - P(AnB) = 21/50 (since either means that we don't want both)

What is wrong here? (OA: 9/20)
_________________

12/2010 GMATPrep 1 620 (Q34/V41)
01/2011 GMATPrep 2 640 (Q42/V36)
01/2011 GMATPrep 3 700 (Q47/V39)
02/2011 GMATPrep 4 710 (Q48/V39)
02/2011 MGMAT CAT 1 650 (Q46/V32)
02/2011 MGMAT CAT 2 680 (Q46/V36)
02/2011 MGMAT CAT 3 710 (Q45/V41)

Intern
Intern
avatar
Joined: 27 Feb 2014
Posts: 11
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 650 Q49 V30
GPA: 3.5
WE: Engineering (Computer Software)
GMAT ToolKit User Premium Member
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 01 Apr 2014, 23:12
@GDR29,

Thanks for the explanation but I have one doubt.

We know that there are two chemistry books and there is no information like atleast each of Maths, Physics and Checmistry has to be either soft or hard covered. In such case, there will be two chemistry books which may be hard covered.

Please advise.
Intern
Intern
avatar
Joined: 02 Apr 2014
Posts: 1
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 02 Apr 2014, 07:22
2
Hi guys,
After knowing there are 20 books on the shelve, I've just used the "Among all the books, 12 books are soft cover and the remaining are hard-cover" info. Using this info you get that 8/20 books are hard cover... and at least one book has to be chemestry, so the chances of getting either a hard cover book or a chemestry one have to be higher than 8/20 --- only alternative is E) 9/20
What do you think?
Thanks!
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8199
Location: Pune, India
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 02 Apr 2014, 22:09
nishant.1987 wrote:
@GDR29,

Thanks for the explanation but I have one doubt.

We know that there are two chemistry books and there is no information like atleast each of Maths, Physics and Checmistry has to be either soft or hard covered. In such case, there will be two chemistry books which may be hard covered.

Please advise.


There is a typo in the question given. You are given that there are 12 softcover books (which means there are 8 hard cover books). You also given that 7 of the hardcover books are either Math or Physics. So there is only 1 Chemistry hard cover book.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8199
Location: Pune, India
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 02 Apr 2014, 22:12
easycheesy wrote:
Hi guys,
After knowing there are 20 books on the shelve, I've just used the "Among all the books, 12 books are soft cover and the remaining are hard-cover" info. Using this info you get that 8/20 books are hard cover... and at least one book has to be chemestry, so the chances of getting either a hard cover book or a chemestry one have to be higher than 8/20 --- only alternative is E) 9/20
What do you think?
Thanks!


That's correct. Note that we do analyze the rest of the data to say that the required probability has to be greater than 8/20 since it is possible that all Chem books are hardcover and hence already a part of the 8 books. But, to say that the required probability is "greater than or equal to" 8/20, all we need is "Among all the books, 12 books are soft cover and the remaining are hard-cover".

There is only one option greater than or equal to 8/20.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
avatar
Joined: 19 Sep 2013
Posts: 3
Location: India
Concentration: Technology
GRE 1: Q161 V162
WE: Engineering (Computer Software)
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 12 May 2014, 00:29
alimad wrote:
Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book?

A. 1/10
B. 3/20
C. 1/5
D. 1/4
E. 9/20

We know that M = 2P
P = 4 + C
M = 8+2C

8 + 2c + 4 + c + c = 20
4c + 12 = 20
4c = 8
c = 2 , P = 6, M = 12

Please assist further. Thanks


Hello
I am not good at probability, but somehow got this answer right . Could you please explain if the approach used by me is correct or it was just a stroke of luck that i got it right..

Number of Math+Physics+Chemistry books= 25 - ((20/100)*25) = 20
Hence, since M=2P, P=4+C,
(4+C)+C+2(4+C)=20
Therefore, M=12, C=2, P=6

Probability of getting a chemistry book = 2/20 = 1/10
Probability of getting a Hardcover book = P(getting a math or phy book) * P( getting a hardcover book from math or phy books) = (18/20 )*(7/18) = 7/20

Therefore, P(Getting chemistry or hardcover book) = (1/10)+(7/20) = 9/20

I am really doubtful about the red colored approach. Please guide.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48067
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 12 May 2014, 03:32
khushboobhatia wrote:
alimad wrote:
Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability, that a book selected at random is either a hard cover book or a chemistry book?

A. 1/10
B. 3/20
C. 1/5
D. 1/4
E. 9/20

We know that M = 2P
P = 4 + C
M = 8+2C

8 + 2c + 4 + c + c = 20
4c + 12 = 20
4c = 8
c = 2 , P = 6, M = 12

Please assist further. Thanks


Hello
I am not good at probability, but somehow got this answer right . Could you please explain if the approach used by me is correct or it was just a stroke of luck that i got it right..

Number of Math+Physics+Chemistry books= 25 - ((20/100)*25) = 20
Hence, since M=2P, P=4+C,
(4+C)+C+2(4+C)=20
Therefore, M=12, C=2, P=6

Probability of getting a chemistry book = 2/20 = 1/10
Probability of getting a Hardcover book = P(getting a math or phy book) * P( getting a hardcover book from math or phy books) = (18/20 )*(7/18) = 7/20

Therefore, P(Getting chemistry or hardcover book) = (1/10)+(7/20) = 9/20

I am really doubtful about the red colored approach. Please guide.


Your approach is correct. Though the red part should be {the probability of getting a hardcover math or physics book}.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
Joined: 03 Jul 2013
Posts: 89
Schools: ISB '17 (A), IIMC (A)
GMAT 1: 660 Q48 V32
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 10 Oct 2014, 19:55
VeritasPrepKarishma wrote:
Mackieman wrote:
Please help me with this one.

Maths, Physics and chemistry books are stored on a library shelf that can accomodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the prob, that a book selected at random is either a hard cover book or a chemistry book?

Chemistry books: 2
Physics books: 6
Math books: 12

Sum = 20

P(Chemistry) = 2/20 = 1/10
P(Hard cover) = 8/20 = 4/10 = 2/5

P(AuB) = P(A)+P(B)-P(AnB)

P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50

P(AuB) = 5/50 + 20/50 - 2/50 = 23/50

P(AuB) - P(AnB) = 21/50 (since either means that we don't want both)

What is wrong here? (OA: 9/20)


Everything is correct except this: P(AnB) = P(A)*(B) = (1/10)*(2/5) = 2/50
P(AnB) is given by the product of individual probabilities when the events are independent.
How many Chemistry books are hardcover? There are total 8 hardcovers and 7 belong to Math and Physics. This means there is only 1 Chemistry hardcover book out of total 20 books.
So P(AnB) = 1/20

Now P(AuB) = 1/10 + 2/5 - 1/20 = 9/20


Hi Karishma. request you to please help me by explaining why the solution is also accounting for the book which is both chemistry and hard cover when the question stem clearly asks we need to select only books which are "Either" chem or hard cover.
_________________

Sometimes standing still can be, the best move you ever make......

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8199
Location: Pune, India
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 12 Oct 2014, 20:57
aadikamagic wrote:
Hi Karishma. request you to please help me by explaining why the solution is also accounting for the book which is both chemistry and hard cover when the question stem clearly asks we need to select only books which are "Either" chem or hard cover.


In Math, 'either or' is interpreted a little differently - it includes the elements which lie in both sets too. "Either Chem or hardcover" means "Chemistry books or hardcover books or both".
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Manager
User avatar
B
Joined: 11 Nov 2011
Posts: 68
Location: United States
Concentration: Finance, Human Resources
GPA: 3.33
WE: Consulting (Non-Profit and Government)
GMAT ToolKit User
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 15 Aug 2015, 04:10
This is a brilliant way of thinking. I really need to develop such ability to get +750. Thanks for sharing easycheesy
Kudos sent

easycheesy wrote:
Hi guys,
After knowing there are 20 books on the shelve, I've just used the "Among all the books, 12 books are soft cover and the remaining are hard-cover" info. Using this info you get that 8/20 books are hard cover... and at least one book has to be chemestry, so the chances of getting either a hard cover book or a chemestry one have to be higher than 8/20 --- only alternative is E) 9/20
What do you think?
Thanks!
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7770
Premium Member
Re: Maths, Physics and chemistry books are stored on a library  [#permalink]

Show Tags

New post 19 Jul 2018, 23:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Maths, Physics and chemistry books are stored on a library &nbs [#permalink] 19 Jul 2018, 23:50
Display posts from previous: Sort by

Maths, Physics and chemistry books are stored on a library

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.